What are the two points of the imaginary axis which satisfy this equation?

Hence sketch the locus of z on this diagram.

My answer:For the two real points I got -5 and 5.Because I ended up with |5| = zSince z = x + yi I thought that y = 0

My queries:
But looking down apparently I was wrong because it then asks for the value of y.

Anybody able to point me in the right direction?

Btw, what is a locus?

A locus is a set of points that satisfies a given relationship. You want the set of points in the complex plane that satisfy .

Geometrically, this is the set of points z such that the distance of z from z = 3 plus the distance of z from z = -3 is equal to 10. Geometrically this defines an ellipse. The points z = 3 and z = -3 are the focal points. The length of the major axis is 10. By symmetry the centre is at (0, 0).

Therefore, if z = x + iy, then the Cartesian equation has the form .

To get b, you can apply Pythagoras Theorem:

Since the focii are at (3, 0) and (-3, 0), .

Therefore the Cartesian equation is .

Of course, you can do it the hard way by substituting z = x + iy into and going through the algebra. If I have time later I'll post the highlights.